Image and video compression have been the object of intensive research in the last thirty years motion estimation is a complex computation found in video compression algorithm such as standard like MPEG-4 and H.263[1][2] Anatural solution is to estimate themotion or displacement field from only two frames and try to compensate for the background motion this paper presents a new transform expansion algorithm to estimate displacement the idea of transform expansion is to approximate some ineighborhood of each pixel with a geometrical transform such as rotation translation scaling and reflection. the result of tranformation expansion is that each neighborhood is approximated by a matrix transform